EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED TYPE INTEGRAL BOUNDARY CONDITIONS

doi:10.1016/S0252-9602(11)60388-3

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (6): 2122-2130.doi: 10.1016/S0252-9602(11)60388-3

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED TYPE INTEGRAL BOUNDARY CONDITIONS

Bashir Ahmad¹| Juan J. Nieto^1,2| Ahmed Alsaedi¹

1. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia;
2. Departamento de An´alisis Matem´atico, Facultad de Matem´aticas, Universidad de Santiago de Compostela, 15782, Santiago de Compostela, Spain

收稿日期:2011-05-04 出版日期:2011-11-20 发布日期:2011-11-20

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED TYPE INTEGRAL BOUNDARY CONDITIONS

Bashir Ahmad¹| Juan J. Nieto^1,2| Ahmed Alsaedi¹

1. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia;
2. Departamento de An´alisis Matem´atico, Facultad de Matem´aticas, Universidad de Santiago de Compostela, 15782, Santiago de Compostela, Spain

Received:2011-05-04 Online:2011-11-20 Published:2011-11-20

摘要/Abstract

摘要：

In this paper, we study a boundary value problem of nonlinear fractional dif-ferential equations of order q (1 < q 2) with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.

关键词: fractional differential equations, non-separated integral boundary condi-tions, contraction principle, Krasnoselskii´s fixed point theorem, Leray-Schauder degree

Abstract:

Key words: fractional differential equations, non-separated integral boundary condi-tions, contraction principle, Krasnoselskii´s fixed point theorem, Leray-Schauder degree

中图分类号:

26A33

Bashir Ahmad, Juan J.Nieto, Ahmed Alsaedi. EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED TYPE INTEGRAL BOUNDARY CONDITIONS[J]. 数学物理学报(英文版), 2011, 31(6): 2122-2130.

Bashir Ahmad, Juan J.Nieto, Ahmed Alsaedi. EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED TYPE INTEGRAL BOUNDARY CONDITIONS[J]. Acta mathematica scientia,Series B, 2011, 31(6): 2122-2130.

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EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED TYPE INTEGRAL BOUNDARY CONDITIONS

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED TYPE INTEGRAL BOUNDARY CONDITIONS

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